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Joint work with Di Fraia and Ramzi. We prove that the functor given by group completion of E_n-monoids in the infinity category of spaces preserves arbitrary products for n at least 2. This proof uses a new approach of obtaining the group completion of an E_n-monoid as the realization of a monoidal infinity-category we call the double action category, which is an unstable analogue of the category of binary complexes due to Grayson. As an application we show that variations of K and L-theory commute with infinite products. In particular, we obtain a new proof of the results of Winges-Kasprowski about K-theory of stable infinity-categories and infinite products.